+91-9350504919 support@wiredfaculty.com
Wired Faculty Logo
Wired Faculty Logo Wired Faculty

Sponsor Area

Integrals

Question
CBSEENMA12032343
Wired Faculty App

Evaluate integral from 1 to 2 of straight x space dx as the limit of a sum.

Solution

Comparing integral from 1 to 2 of straight x space dx space space with space integral from straight a to straight b of straight f left parenthesis straight x right parenthesis space dx comma space space we space get comma
               WiredFaculty
therefore space space space straight f left parenthesis straight a right parenthesis space equals space straight a comma space space straight f left parenthesis straight a plus straight h right parenthesis space equals space straight a plus straight h comma space space straight f left parenthesis straight a plus 2 straight h right parenthesis space equals space straight a plus 2 straight h comma space...... straight f left parenthesis straight a plus stack straight n minus 1 with bar on top straight h right parenthesis space equals space straight a plus left parenthesis straight n minus 1 right parenthesis straight h
Now   integral from straight a to straight b of straight f left parenthesis straight x right parenthesis space equals space stack Lt. straight h with straight h rightwards arrow 0 below left square bracket space straight f left parenthesis straight a right parenthesis plus straight f left parenthesis straight a plus straight h right parenthesis plus straight f left parenthesis straight a plus 2 straight h right parenthesis space plus space....... plus straight f left parenthesis straight a plus stack straight n minus 1 with bar on top space straight h right parenthesis right square bracket
                                                                                              where n h = b - a
rightwards double arrow        integral from straight a to straight b of xdx space equals space Lt with straight h rightwards arrow 0 below straight h left square bracket straight a plus straight a left parenthesis straight a plus straight h right parenthesis plus left parenthesis straight a plus 2 space straight h right parenthesis space plus space... plus left parenthesis straight a plus stack straight n minus 1 with bar on top straight h right parenthesis right square bracket
                          equals stack Lt space straight h with straight h rightwards arrow 0 below left square bracket left parenthesis straight a plus straight a plus straight a plus... to space straight n space terms right parenthesis space plus space straight h open curly brackets 1 plus 2 plus 3 plus.... plus left parenthesis straight n minus 1 right parenthesis close curly brackets right square bracket
                         WiredFaculty
therefore space space space space space integral from straight a to straight b of xdx space equals space 1 half left parenthesis straight b squared minus straight a squared right parenthesis
Put a = 1,  b = 2
therefore space space space space space space space space space space space space space integral from 1 to 2 of xdx space equals space 1 half left parenthesis 4 minus 1 right parenthesis space equals space 3 over 2

Some More Questions From Integrals Chapter

Sponsor Area

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation